Notes 9-5: Simplifying Complex Numbers a + bi is a complex number in rectangular form where a and b are real numbers and i is an imaginary number. Reminder: 1 i repeating pattern (cycle of 4 values) -1 -i 1

To simplify imaginary numbers with exponents, it is often useful to divide the exponent by 4 and then look at the value of the remainder: so your answer is: remainder: (after dividing by 4) corresponds to:

Examples: i -1

turn it into a positive value. -1 What do we do with a negative remainder? Add one “cycle” of 4 to turn it into a positive value. remainder -1 is the same as -1 + 4 = remainder 3